This project involves collaborative research with NIH scientists, in which the research requires sophisticated mathematical tools or an acquaintance with theoretical methods in the physical sciences. Four major projects are current. One is with Drs. Sergei Bezrukov of the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) and Alexander Berezhkovskii of the National Institute of Child Health and Human Development (NICHD) on the development of models with which to interpret experimental results on the transport of ions through biological membranes. The second and third are with Dr. Attila Szabo (NIDDK). The first of these relates to the development of theoretical models for chemical reaction rates, and the second to developing the theory necessary for interpreting experimental measurements made using the technique of single-molecule spectroscopy. A fourth project is devoted to developing theory related to optical imaging techniques, together with Dr. A.H. Gandjbakhche (NIDDK). In this we have devised a model to estimate parameters that serve to characterize photon trajectories in continuous-wave measurements. - ion transport, membranes, reaction rates, spectroscopy, imaging, continuous-wave, measurements, optical